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On algebraic automorphisms and their rational invariants

Bonnet, Philippe

In: Transformation Groups, 2007, vol. 12, no. 4, p. 619-630

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    Titre
    • On algebraic automorphisms and their rational invariants
    Auteur
    • Bonnet, Philippe. Mathematisches Institut, Universitat Basel, Rheinsprung 21, 4051, Basel, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Transformation Groups, 2007, vol. 12, no. 4, p. 619-630. Birkhäuser-Verlag; www.birkhauser.com
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319863
    Summary
    Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism Φ, we denote by k(X)Φ its field of invariants, i.e., the set of rational functions f on X such that f º Φ = f. Let n(Φ) be the transcendence degree of k(X)Φ over k. In this paper we study the class of automorphisms Φ of X for which n(Φ) = dim X - 1. More precisely, we show that under some conditions on X, every such automorphism is of the form Φ = ϕg, where ϕ is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G. As an application, we determine the conjugacy classes of automorphisms of the plane for which n(Φ) = 1